Jude T. Anderson , David M. Williams , Andrew Corrigan
{"title":"时空有限元方法的曲面和超曲面网格划分技术","authors":"Jude T. Anderson , David M. Williams , Andrew Corrigan","doi":"10.1016/j.cad.2023.103574","DOIUrl":null,"url":null,"abstract":"<div><p>A novel method is introduced for constructing two-dimensional (2D) surface meshes embedded in three-dimensional (3D) space time <em>and</em> 3D hypersurface meshes embedded in four-dimensional (4D) space time. In particular, we begin by dividing the space–time domain into time slabs. Each time slab is equipped with an initial plane (hyperplane), in conjunction with an unstructured simplicial surface (hypersurface) mesh that covers the initial plane. We then obtain the vertices of the terminating plane (hyperplane) of the time slab from the vertices of the initial plane using a space–time trajectory-tracking approach. Next, these vertices are used to create an unstructured simplicial mesh on the terminating plane (hyperplane). Thereafter, the initial and terminating boundary vertices are stitched together to form simplicial meshes on the intermediate surfaces or <em>sides</em> of the time slab. After describing this new mesh-generation method in rigorous detail, we provide the results of multiple numerical experiments which demonstrate its validity and flexibility.</p></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":null,"pages":null},"PeriodicalIF":3.0000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Surface And Hypersurface Meshing Techniques for Space–Time Finite Element Methods\",\"authors\":\"Jude T. Anderson , David M. Williams , Andrew Corrigan\",\"doi\":\"10.1016/j.cad.2023.103574\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A novel method is introduced for constructing two-dimensional (2D) surface meshes embedded in three-dimensional (3D) space time <em>and</em> 3D hypersurface meshes embedded in four-dimensional (4D) space time. In particular, we begin by dividing the space–time domain into time slabs. Each time slab is equipped with an initial plane (hyperplane), in conjunction with an unstructured simplicial surface (hypersurface) mesh that covers the initial plane. We then obtain the vertices of the terminating plane (hyperplane) of the time slab from the vertices of the initial plane using a space–time trajectory-tracking approach. Next, these vertices are used to create an unstructured simplicial mesh on the terminating plane (hyperplane). Thereafter, the initial and terminating boundary vertices are stitched together to form simplicial meshes on the intermediate surfaces or <em>sides</em> of the time slab. After describing this new mesh-generation method in rigorous detail, we provide the results of multiple numerical experiments which demonstrate its validity and flexibility.</p></div>\",\"PeriodicalId\":50632,\"journal\":{\"name\":\"Computer-Aided Design\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.0000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computer-Aided Design\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0010448523001069\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"COMPUTER SCIENCE, SOFTWARE ENGINEERING\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer-Aided Design","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0010448523001069","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
Surface And Hypersurface Meshing Techniques for Space–Time Finite Element Methods
A novel method is introduced for constructing two-dimensional (2D) surface meshes embedded in three-dimensional (3D) space time and 3D hypersurface meshes embedded in four-dimensional (4D) space time. In particular, we begin by dividing the space–time domain into time slabs. Each time slab is equipped with an initial plane (hyperplane), in conjunction with an unstructured simplicial surface (hypersurface) mesh that covers the initial plane. We then obtain the vertices of the terminating plane (hyperplane) of the time slab from the vertices of the initial plane using a space–time trajectory-tracking approach. Next, these vertices are used to create an unstructured simplicial mesh on the terminating plane (hyperplane). Thereafter, the initial and terminating boundary vertices are stitched together to form simplicial meshes on the intermediate surfaces or sides of the time slab. After describing this new mesh-generation method in rigorous detail, we provide the results of multiple numerical experiments which demonstrate its validity and flexibility.
期刊介绍:
Computer-Aided Design is a leading international journal that provides academia and industry with key papers on research and developments in the application of computers to design.
Computer-Aided Design invites papers reporting new research, as well as novel or particularly significant applications, within a wide range of topics, spanning all stages of design process from concept creation to manufacture and beyond.